{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analyzing out-of-this world data\n",
    "Using data collected from the Open Exoplanet Catalogue database: https://github.com/OpenExoplanetCatalogue/open_exoplanet_catalogue/\n",
    "\n",
    "## Data License\n",
    "Copyright (C) 2012 Hanno Rein\n",
    "\n",
    "Permission is hereby granted, free of charge, to any person obtaining a copy of this database and associated scripts (the \"Database\"), to deal in the Database without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Database, and to permit persons to whom the Database is furnished to do so, subject to the following conditions:\n",
    "\n",
    "The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Database. A reference to the Database shall be included in all scientific publications that make use of the Database.\n",
    "\n",
    "THE DATABASE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE DATABASE OR THE USE OR OTHER DEALINGS IN THE DATABASE."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EDA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "planets = pd.read_csv('data/planets.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>period</th>\n",
       "      <th>name</th>\n",
       "      <th>eccentricity</th>\n",
       "      <th>description</th>\n",
       "      <th>discoverymethod</th>\n",
       "      <th>periastrontime</th>\n",
       "      <th>lastupdate</th>\n",
       "      <th>semimajoraxis</th>\n",
       "      <th>mass</th>\n",
       "      <th>periastron</th>\n",
       "      <th>list</th>\n",
       "      <th>discoveryyear</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>326.03</td>\n",
       "      <td>11 Com b</td>\n",
       "      <td>0.231</td>\n",
       "      <td>11 Com b is a brown dwarf-mass companion to th...</td>\n",
       "      <td>RV</td>\n",
       "      <td>2452899.60</td>\n",
       "      <td>15/09/20</td>\n",
       "      <td>1.290</td>\n",
       "      <td>19.400</td>\n",
       "      <td>94.800</td>\n",
       "      <td>Confirmed planets</td>\n",
       "      <td>2008.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>516.22</td>\n",
       "      <td>11 UMi b</td>\n",
       "      <td>0.080</td>\n",
       "      <td>11 Ursae Minoris is a star located in the cons...</td>\n",
       "      <td>RV</td>\n",
       "      <td>2452861.04</td>\n",
       "      <td>15/09/20</td>\n",
       "      <td>1.540</td>\n",
       "      <td>11.200</td>\n",
       "      <td>117.630</td>\n",
       "      <td>Confirmed planets</td>\n",
       "      <td>2009.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>185.84</td>\n",
       "      <td>14 And b</td>\n",
       "      <td>0.000</td>\n",
       "      <td>14 Andromedae is an evolved star in the conste...</td>\n",
       "      <td>RV</td>\n",
       "      <td>2452861.40</td>\n",
       "      <td>15/09/20</td>\n",
       "      <td>0.830</td>\n",
       "      <td>4.800</td>\n",
       "      <td>0.000</td>\n",
       "      <td>Confirmed planets</td>\n",
       "      <td>2008.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1766.00</td>\n",
       "      <td>14 Her b</td>\n",
       "      <td>0.359</td>\n",
       "      <td>The star 14 Herculis is only 59 light years aw...</td>\n",
       "      <td>RV</td>\n",
       "      <td>NaN</td>\n",
       "      <td>15/09/21</td>\n",
       "      <td>2.864</td>\n",
       "      <td>4.975</td>\n",
       "      <td>22.230</td>\n",
       "      <td>Confirmed planets</td>\n",
       "      <td>2002.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>9886.00</td>\n",
       "      <td>14 Her c</td>\n",
       "      <td>0.184</td>\n",
       "      <td>14 Her c is the second companion in the system...</td>\n",
       "      <td>RV</td>\n",
       "      <td>NaN</td>\n",
       "      <td>15/09/21</td>\n",
       "      <td>9.037</td>\n",
       "      <td>7.679</td>\n",
       "      <td>189.076</td>\n",
       "      <td>Controversial</td>\n",
       "      <td>2006.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    period      name  eccentricity  \\\n",
       "0   326.03  11 Com b         0.231   \n",
       "1   516.22  11 UMi b         0.080   \n",
       "2   185.84  14 And b         0.000   \n",
       "3  1766.00  14 Her b         0.359   \n",
       "4  9886.00  14 Her c         0.184   \n",
       "\n",
       "                                         description discoverymethod  \\\n",
       "0  11 Com b is a brown dwarf-mass companion to th...              RV   \n",
       "1  11 Ursae Minoris is a star located in the cons...              RV   \n",
       "2  14 Andromedae is an evolved star in the conste...              RV   \n",
       "3  The star 14 Herculis is only 59 light years aw...              RV   \n",
       "4  14 Her c is the second companion in the system...              RV   \n",
       "\n",
       "   periastrontime lastupdate  semimajoraxis    mass  periastron  \\\n",
       "0      2452899.60   15/09/20          1.290  19.400      94.800   \n",
       "1      2452861.04   15/09/20          1.540  11.200     117.630   \n",
       "2      2452861.40   15/09/20          0.830   4.800       0.000   \n",
       "3             NaN   15/09/21          2.864   4.975      22.230   \n",
       "4             NaN   15/09/21          9.037   7.679     189.076   \n",
       "\n",
       "                list  discoveryyear  \n",
       "0  Confirmed planets         2008.0  \n",
       "1  Confirmed planets         2009.0  \n",
       "2  Confirmed planets         2008.0  \n",
       "3  Confirmed planets         2002.0  \n",
       "4      Controversial         2006.0  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "planets.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Looking for correlated features\n",
    "It's important to perform an in-depth exploration of the data before modeling. This includes consulting domain experts, looking for correlations between variables, examining distributions, etc. The visualizations covered in chapters [5](https://github.com/stefmolin/Hands-On-Data-Analysis-with-Pandas/tree/master/ch_05) and [6](https://github.com/stefmolin/Hands-On-Data-Analysis-with-Pandas/tree/master/ch_06) will prove indispensible for this process. One such visualization is the heatmap which we can use to look for correlated features:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x56fd0b0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(7, 7))\n",
    "sns.heatmap(\n",
    "    planets.drop(columns='discoveryyear').corr(), \n",
    "    center=0, square=True, annot=True\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Looking at Orbit shape\n",
    "(0, 1) is elliptical, 0 is perfect circle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Exoplanet Eccentricities')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "planets.eccentricity.hist()\n",
    "plt.xlabel('eccentricity')\n",
    "plt.ylabel('frequency')\n",
    "plt.title('Exoplanet Eccentricities')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 0.956)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "planets.eccentricity.min(), planets.eccentricity.max()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Understanding the semi-major axis\n",
    "An ellipse, being an elongated circle has 2 axes: **major** and **minor** for the longest and smallest ones, respectively. The *semi*-major axis is half the major axis. When compared to a circle, the axes are like the diameter crossing the entire shape and the semis are akin to the radius being half the diameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11e70910>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.patches import Ellipse\n",
    "\n",
    "fig, axes = plt.subplots(1, 1)\n",
    "orbit = Ellipse(xy=(0, 0), width=2, height=1.5, facecolor='lightblue')\n",
    "axes.add_artist(orbit)\n",
    "axes.plot([-1, 0], [0, 0])\n",
    "axes.annotate(\n",
    "    'semi-major axis', \n",
    "    xy=(-0.5, 0), \n",
    "    xytext=(-0.8, -0.2), \n",
    "    arrowprops=dict(arrowstyle='wedge')\n",
    ")\n",
    "axes.annotate(\n",
    "    'orbit center', \n",
    "    xy=(0, 0), \n",
    "    xytext=(-0.21, 0.115), \n",
    "    arrowprops=dict(arrowstyle='wedge')\n",
    ")\n",
    "plt.plot(\n",
    "    [-.75], [0.5], \n",
    "    marker='o', markersize=4, \n",
    "    color='green', label='planet'\n",
    ")\n",
    "plt.plot(\n",
    "    [0], [0], \n",
    "    marker='o', markersize=10, \n",
    "    color='orange', label='star'\n",
    ")\n",
    "plt.xlim(-1.25, 1.25)\n",
    "plt.ylim(-1.25, 1.25)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Checking data values\n",
    "With just the variables of interest, we have a lot of missing data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 3814 entries, 0 to 3813\n",
      "Data columns (total 4 columns):\n",
      "period           3684 non-null float64\n",
      "eccentricity     1172 non-null float64\n",
      "semimajoraxis    1456 non-null float64\n",
      "mass             1417 non-null float64\n",
      "dtypes: float64(4)\n",
      "memory usage: 119.2 KB\n"
     ]
    }
   ],
   "source": [
    "planets[['period', 'eccentricity', 'semimajoraxis', 'mass']].info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we drop it, we are left with about a third of it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1044, 4)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "planets[['period', 'eccentricity', 'semimajoraxis', 'mass']].dropna().shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use `describe()` to get a summary of the variables of interest:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>period</th>\n",
       "      <th>eccentricity</th>\n",
       "      <th>semimajoraxis</th>\n",
       "      <th>mass</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>3684.000000</td>\n",
       "      <td>1172.000000</td>\n",
       "      <td>1456.000000</td>\n",
       "      <td>1417.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>517.715911</td>\n",
       "      <td>0.168518</td>\n",
       "      <td>1.610329</td>\n",
       "      <td>2.837145</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>7284.863699</td>\n",
       "      <td>0.190131</td>\n",
       "      <td>8.282760</td>\n",
       "      <td>9.043661</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.090706</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.004420</td>\n",
       "      <td>0.000008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>4.725905</td>\n",
       "      <td>0.020000</td>\n",
       "      <td>0.052530</td>\n",
       "      <td>0.141600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>12.878744</td>\n",
       "      <td>0.109000</td>\n",
       "      <td>0.163518</td>\n",
       "      <td>0.914000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>48.350875</td>\n",
       "      <td>0.250000</td>\n",
       "      <td>1.250000</td>\n",
       "      <td>2.540000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>320000.000000</td>\n",
       "      <td>0.956000</td>\n",
       "      <td>177.000000</td>\n",
       "      <td>263.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              period  eccentricity  semimajoraxis         mass\n",
       "count    3684.000000   1172.000000    1456.000000  1417.000000\n",
       "mean      517.715911      0.168518       1.610329     2.837145\n",
       "std      7284.863699      0.190131       8.282760     9.043661\n",
       "min         0.090706      0.000000       0.004420     0.000008\n",
       "25%         4.725905      0.020000       0.052530     0.141600\n",
       "50%        12.878744      0.109000       0.163518     0.914000\n",
       "75%        48.350875      0.250000       1.250000     2.540000\n",
       "max    320000.000000      0.956000     177.000000   263.000000"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "planets[['period', 'eccentricity', 'semimajoraxis', 'mass']].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing Year and Orbit Length\n",
    "We have information on the planet list each planet belongs to. We may be wondering if these planets controversial because they are so far away?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10db1210>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = sns.scatterplot(planets.semimajoraxis, planets.period, hue=planets.list, alpha=0.5)\n",
    "plt.title('period vs. semimajoraxis')\n",
    "ax.legend(bbox_to_anchor=(1, 0.77)) # move legend to the right of the plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since semi-major axis is highly correlated with period, let's see how the planets compare and label those in our solar system:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'log(orbital period) vs. semi-major axis')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 1, figsize=(10, 10))\n",
    "in_solar_system = (planets.list == 'Solar System').rename('in solar system?')\n",
    "ax = sns.scatterplot(\n",
    "    planets.semimajoraxis, \n",
    "    planets.period, \n",
    "    hue=in_solar_system,\n",
    "    ax=axes\n",
    ")\n",
    "ax.set_yscale('log')\n",
    "solar_system = planets[planets.list == 'Solar System']\n",
    "for planet in solar_system.name:\n",
    "    data = solar_system.query(f'name == \"{planet}\"')\n",
    "    ax.annotate(\n",
    "        planet, \n",
    "        (data.semimajoraxis, data.period), \n",
    "        (7 + data.semimajoraxis, data.period),\n",
    "        arrowprops=dict(arrowstyle='->')\n",
    "    )\n",
    "ax.set_title('log(orbital period) vs. semi-major axis')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Finding Similar Planets with k-Means Clustering\n",
    "Since we want to perform clustering to learn more about the data, we will build our pipeline standardizing the data before running k-means and fit it on the all the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "kmeans_pipeline = Pipeline(\n",
    "    [\n",
    "        ('scale', StandardScaler()), \n",
    "        ('kmeans', KMeans(8, random_state=0))\n",
    "    ]\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Grab the data and fit the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "     steps=[('scale', StandardScaler(copy=True, with_mean=True, with_std=True)), ('kmeans', KMeans(algorithm='auto', copy_x=True, init='k-means++', max_iter=300,\n",
       "    n_clusters=8, n_init=10, n_jobs=None, precompute_distances='auto',\n",
       "    random_state=0, tol=0.0001, verbose=0))])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kmeans_data = planets[['semimajoraxis', 'period']].dropna()\n",
    "kmeans_pipeline.fit(kmeans_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can recreate our plot from before and this time, color by the cluster k-means put each planet in:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'KMeans Clusters')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 1, figsize=(7, 7))\n",
    "ax = sns.scatterplot(\n",
    "    kmeans_data.semimajoraxis, \n",
    "    kmeans_data.period, \n",
    "    hue=kmeans_pipeline.predict(kmeans_data),\n",
    "    ax=axes, palette='Accent'\n",
    ")\n",
    "ax.set_yscale('log')\n",
    "solar_system = planets[planets.list == 'Solar System']\n",
    "for planet in solar_system.name:\n",
    "    data = solar_system.query(f'name == \"{planet}\"')\n",
    "    ax.annotate(\n",
    "        planet, \n",
    "        (data.semimajoraxis, data.period), \n",
    "        (7 + data.semimajoraxis, data.period),\n",
    "        arrowprops=dict(arrowstyle='->')\n",
    "    )\n",
    "ax.get_legend().remove()\n",
    "ax.set_title('KMeans Clusters')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The elbow point method can be used to pick a good value for `k`. This value will be were we begin to see diminishing returns in the reduction of the value of the objective function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(4.5, 1450, '')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ml_utils.elbow_point import elbow_point\n",
    "\n",
    "ax = elbow_point(\n",
    "    kmeans_data, \n",
    "    Pipeline([\n",
    "        ('scale', StandardScaler()), \n",
    "        ('kmeans', KMeans(random_state=0))\n",
    "    ])\n",
    ")\n",
    "ax.annotate(\n",
    "    'possible appropriate values for k', xy=(2, 730), xytext=(2.5, 1500), \n",
    "    arrowprops=dict(arrowstyle='->')\n",
    ")\n",
    "ax.annotate(\n",
    "    '', xy=(3, 350), xytext=(4.5, 1450), arrowprops=dict(arrowstyle='->')\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "k-means with the \"optimal\" k of 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'KMeans Clusters')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeans_pipeline_2 = Pipeline(\n",
    "    [\n",
    "        ('scale', StandardScaler()), \n",
    "        ('kmeans', KMeans(2, random_state=0))\n",
    "    ]\n",
    ").fit(kmeans_data)\n",
    "fig, axes = plt.subplots(1, 1, figsize=(7, 7))\n",
    "ax = sns.scatterplot(\n",
    "    kmeans_data.semimajoraxis, \n",
    "    kmeans_data.period, \n",
    "    hue=kmeans_pipeline_2.predict(kmeans_data),\n",
    "    ax=axes, palette='Accent'\n",
    ")\n",
    "ax.set_yscale('log')\n",
    "solar_system = planets[planets.list == 'Solar System']\n",
    "for planet in solar_system.name:\n",
    "    data = solar_system.query(f'name == \"{planet}\"')\n",
    "    ax.annotate(\n",
    "        planet, \n",
    "        (data.semimajoraxis, data.period), \n",
    "        (7 + data.semimajoraxis, data.period),\n",
    "        arrowprops=dict(arrowstyle='->')\n",
    "    )\n",
    "ax.get_legend().remove()\n",
    "ax.set_title('KMeans Clusters')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing the cluster space\n",
    "Since we standardized the data, looking at the centers tells us the second cluster contains \"outliers\" for period and semi-major axis:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.03757155, -0.04116566],\n",
       "       [17.84648778, 19.55368709]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kmeans_pipeline_2.named_steps['kmeans'].cluster_centers_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also visualize the clusters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set up layout\n",
    "fig = plt.figure(figsize=(8, 6))\n",
    "outside = fig.add_axes([0.1, 0.1, 0.9, 0.9])\n",
    "inside = fig.add_axes([0.6, 0.2, 0.35, 0.35])\n",
    "\n",
    "# scaled data and cluster distance data\n",
    "scaled = kmeans_pipeline_2.named_steps['scale'].fit_transform(\n",
    "    kmeans_data\n",
    ")\n",
    "cluster_distances = kmeans_pipeline_2.fit_transform(\n",
    "    kmeans_data\n",
    ")\n",
    "\n",
    "for ax, data, title, axes_labels in zip(\n",
    "    [outside, inside], [scaled, cluster_distances],  \n",
    "    ['Visualizing Clusters', 'Cluster Distance Space'], \n",
    "    ['standardized', 'distance to centroid']\n",
    "):\n",
    "    ax = sns.scatterplot(\n",
    "        data[:,0], data[:,1], ax=ax, palette='Accent', alpha=0.5,\n",
    "        hue=kmeans_pipeline_2.named_steps['kmeans'].labels_, s=100\n",
    "    )\n",
    "\n",
    "    ax.get_legend().remove()\n",
    "    ax.set_title(title)\n",
    "    ax.set_xlabel(f'semimajoraxis ({axes_labels})')\n",
    "    ax.set_ylabel(f'period ({axes_labels})')\n",
    "    ax.set_ylim(-1, None)\n",
    "    \n",
    "# add the centroids to the outside plot\n",
    "cluster_centers = kmeans_pipeline_2.named_steps['kmeans']\\\n",
    "                    .cluster_centers_\n",
    "for color, centroid in zip(['green', 'purple'], cluster_centers):\n",
    "    outside.plot(*centroid, color=color, marker='x')\n",
    "    outside.annotate(\n",
    "        f'{color} center', xy=centroid, xytext=centroid + [0, 5], \n",
    "        arrowprops=dict(arrowstyle='->')\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Evaluation of model\n",
    "There are many metrics to choose from, but since we don't know the true labels of our data, we can only use unsupervised ones. We will use a few different metrics to get a more well-rounded view of our performance:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Silhouette Score\n",
    "- true labels not known\n",
    "- higher = better defined (more separated) clusters\n",
    "- -1 is worst, 1 is best, near 0 indicates overlapping clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.756431346264896"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import silhouette_score\n",
    "silhouette_score(kmeans_data, kmeans_pipeline.predict(kmeans_data)) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Davies-Bouldin Score\n",
    "- true labels not known\n",
    "- ratio of within-cluster distances to between-cluster distances\n",
    "- zero is best parition "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\users\\molinstefanie\\packt\\venv\\lib\\site-packages\\sklearn\\metrics\\cluster\\unsupervised.py:342: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  score = (intra_dists[:, None] + intra_dists) / centroid_distances\n",
      "c:\\users\\molinstefanie\\packt\\venv\\lib\\site-packages\\sklearn\\metrics\\cluster\\unsupervised.py:342: RuntimeWarning: invalid value encountered in true_divide\n",
      "  score = (intra_dists[:, None] + intra_dists) / centroid_distances\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.4432430729371101"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import davies_bouldin_score\n",
    "davies_bouldin_score(kmeans_data, kmeans_pipeline.predict(kmeans_data)) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Calinski and Harabaz Score\n",
    "- true labels not known\n",
    "- higher = better defined (more separated) clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "23153.731441632073"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import calinski_harabaz_score\n",
    "calinski_harabaz_score(kmeans_data, kmeans_pipeline.predict(kmeans_data)) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Predicting Length of Year in Earth Days (Period)\n",
    "1. separate x and y data, dropping nulls\n",
    "2. create the training and testing sets\n",
    "3. train a linear regression model (no pipeline since we want to interpret the coefficients)\n",
    "4. isolate the coefficients from the model\n",
    "5. evaluate the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "# 1\n",
    "data = planets[\n",
    "    ['semimajoraxis', 'period', 'mass', 'eccentricity']\n",
    "].dropna()\n",
    "X = data[['semimajoraxis', 'mass', 'eccentricity']]\n",
    "y = data.period\n",
    "\n",
    "# 2\n",
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    X, y, test_size=0.25, random_state=0\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 3\n",
    "lm = LinearRegression().fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Get equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1016.9414328876608"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get intercept\n",
    "lm.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('semimajoraxis', 2089.7990582230304),\n",
       " ('mass', -11.450731945992032),\n",
       " ('eccentricity', -4000.9101385815848)]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 4. get coefficients\n",
    "[(col, coef) for col, coef in zip(X_train.columns, lm.coef_)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluation of model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9766538595075525"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 5\n",
    "preds = lm.predict(X_test)\n",
    "np.corrcoef(y_test, preds)[0][1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0.98, 'Linear Regression')"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 1, figsize=(5, 3))\n",
    "axes.plot(X_test.semimajoraxis, y_test, 'bo', label='actuals', alpha=0.5)\n",
    "axes.plot(X_test.semimajoraxis, preds, 'ro', label='predictions', alpha=0.5)\n",
    "plt.xlabel('semimajoraxis')\n",
    "plt.ylabel('period')\n",
    "plt.legend()\n",
    "plt.suptitle('Linear Regression')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([<matplotlib.axes._subplots.AxesSubplot object at 0x13647FB0>,\n",
       "       <matplotlib.axes._subplots.AxesSubplot object at 0x1308E490>],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ml_utils.regression import plot_residuals\n",
    "\n",
    "plot_residuals(y_test, preds)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### R-squared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9297571053513579"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9297571053513579"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import r2_score\n",
    "r2_score(y_test, preds)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Adjusted R-squared\n",
    "R-squared increases when we add regressors whether or not they actually improve the model. Adjusted R-squared penalizes additional regressors to address this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9289371493826968"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from ml_utils.regression import adjusted_r2\n",
    "adjusted_r2(lm, X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problems with R-squared\n",
    "R-squared doesn't tell us about the prediction errors or if we specified the model correctly. Consider Anscombe's quartet from [chapter 1](https://github.com/stefmolin/Hands-On-Data-Analysis-with-Pandas/blob/master/ch_01/introduction_to_data_analysis.ipynb):\n",
    "\n",
    "##### Anscombe's Quartet\n",
    "All four data sets have the same summary statistics (mean, standard deviation, correlation coefficient), despite having different data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"8\" halign=\"left\">x</th>\n",
       "      <th colspan=\"8\" halign=\"left\">y</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dataset</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>I</th>\n",
       "      <td>11.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>3.316625</td>\n",
       "      <td>4.0</td>\n",
       "      <td>6.5</td>\n",
       "      <td>9.0</td>\n",
       "      <td>11.5</td>\n",
       "      <td>14.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>7.500909</td>\n",
       "      <td>2.031568</td>\n",
       "      <td>4.26</td>\n",
       "      <td>6.315</td>\n",
       "      <td>7.58</td>\n",
       "      <td>8.57</td>\n",
       "      <td>10.84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>II</th>\n",
       "      <td>11.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>3.316625</td>\n",
       "      <td>4.0</td>\n",
       "      <td>6.5</td>\n",
       "      <td>9.0</td>\n",
       "      <td>11.5</td>\n",
       "      <td>14.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>7.500909</td>\n",
       "      <td>2.031657</td>\n",
       "      <td>3.10</td>\n",
       "      <td>6.695</td>\n",
       "      <td>8.14</td>\n",
       "      <td>8.95</td>\n",
       "      <td>9.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>III</th>\n",
       "      <td>11.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>3.316625</td>\n",
       "      <td>4.0</td>\n",
       "      <td>6.5</td>\n",
       "      <td>9.0</td>\n",
       "      <td>11.5</td>\n",
       "      <td>14.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>7.500000</td>\n",
       "      <td>2.030424</td>\n",
       "      <td>5.39</td>\n",
       "      <td>6.250</td>\n",
       "      <td>7.11</td>\n",
       "      <td>7.98</td>\n",
       "      <td>12.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IV</th>\n",
       "      <td>11.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>3.316625</td>\n",
       "      <td>8.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>19.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>7.500909</td>\n",
       "      <td>2.030579</td>\n",
       "      <td>5.25</td>\n",
       "      <td>6.170</td>\n",
       "      <td>7.04</td>\n",
       "      <td>8.19</td>\n",
       "      <td>12.50</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            x                                               y            \\\n",
       "        count mean       std  min  25%  50%   75%   max count      mean   \n",
       "dataset                                                                   \n",
       "I        11.0  9.0  3.316625  4.0  6.5  9.0  11.5  14.0  11.0  7.500909   \n",
       "II       11.0  9.0  3.316625  4.0  6.5  9.0  11.5  14.0  11.0  7.500909   \n",
       "III      11.0  9.0  3.316625  4.0  6.5  9.0  11.5  14.0  11.0  7.500000   \n",
       "IV       11.0  9.0  3.316625  8.0  8.0  8.0   8.0  19.0  11.0  7.500909   \n",
       "\n",
       "                                                   \n",
       "              std   min    25%   50%   75%    max  \n",
       "dataset                                            \n",
       "I        2.031568  4.26  6.315  7.58  8.57  10.84  \n",
       "II       2.031657  3.10  6.695  8.14  8.95   9.26  \n",
       "III      2.030424  5.39  6.250  7.11  7.98  12.74  \n",
       "IV       2.030579  5.25  6.170  7.04  8.19  12.50  "
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "anscombe = sns.load_dataset('anscombe').groupby('dataset')\n",
    "anscombe.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When fitted with a regression line, they all have the same R-squared despite some of them not indicating a linear relationship between x and y:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0.95, \"Anscombe's Quartet\")"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import r2_score\n",
    "\n",
    "fig, axes = plt.subplots(2, 2, figsize=(12, 12))\n",
    "axes = axes.flatten()\n",
    "titles = ['linear', 'non-linear', 'linear with outlier', 'vertical with outlier']\n",
    "\n",
    "for ax, (group_name, group_data), title in zip(axes, anscombe, titles):\n",
    "    x, y = group_data.x, group_data.y\n",
    "    ax.scatter(x, y)\n",
    "    ax.set_title(f'{group_name} - {title}')\n",
    "    ax.set_xlabel('x')\n",
    "    ax.set_ylabel('y')\n",
    "    ax.set_xlim((3, 19.5))\n",
    "    ax.set_ylim((2, 13))\n",
    "    \n",
    "    # get regression line\n",
    "    m, b = np.polyfit(x, y, 1)\n",
    "    reg_x = np.append([0, 20], x)\n",
    "    reg_y = [m*num + b for num in reg_x]\n",
    "    ax.plot(reg_x, reg_y, 'r--')\n",
    "    ax.annotate(\n",
    "        f\"\"\"ρ = {np.corrcoef(x,y)[0][1]:.2}\\ny = {m:.2}x + {b:.2}\\n\\n{\n",
    "            r'$R^2$'\n",
    "        } = {r2_score(y, [m*num + b for num in x]):.2}\\n\\n{\n",
    "            r'$μ_x$'\n",
    "        } = {np.mean(x):2} | {\n",
    "            r'$σ_x$'\n",
    "        } = {np.std(x):.2}\\n{\n",
    "            r'$μ_y$'\n",
    "        } = {np.mean(y):.2} | {r'$σ_y$'} = {np.std(y):.2}\"\"\", xy=(13, 2.5)\n",
    "    )\n",
    "plt.suptitle(\"Anscombe's Quartet\", fontsize=16, y=0.95)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Explained Variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9304626837290991"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import explained_variance_score\n",
    "explained_variance_score(y_test, preds)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Mean Absolute Error (MAE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1396.404208388504"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import mean_absolute_error\n",
    "mean_absolute_error(y_test, preds)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Root Mean Squared Error (RMSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1777.2717945732813"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "np.sqrt(mean_squared_error(y_test, preds))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Median Absolute Error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1080.3627726120715"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import median_absolute_error\n",
    "median_absolute_error(y_test, preds)"
   ]
  }
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